Most Iraqis voted for provincial councils in April but the Shi'ite-led government postponed elections in Anbar and Nineveh, citing security concerns after months of protests by the country's Sunni minority.

The decision to delay voting in those governorates was criticized by the United States, which said it would compound a sense of Sunni marginalization that has fuelled a wave of violent unrest.

More than 1,000 people were killed in militant attacks in Iraq in May, making it the deadliest month since the height of sectarian bloodletting in 2006-07.

The suicide bomber blew himself up at a vote-counting center in the city of Ramadi in Anbar province, killing seven people, four of whom were members of Iraq's electoral commission.

Earlier on Thursday, a roadside bomb hit a bus carrying five electoral officials in the town of Baiji in Nineveh, killing one, police said. In the provincial capital Mosul, a mortar round was fired at a checkpoint near a voting center, wounding two soldiers.

On Wednesday, a suicide bomber embraced and killed a Sunni political leader, also in Nineveh.

"The people of Anbar and Nineveh overcame threats to cast their vote today, and violence failed to disrupt the democratic process," United Nations envoy to Iraq Martin Kobler said in a statement.

The first ballot to be held since U.S. troops left the country will indicate the strength of Iraq's Sunni political groupings before a parliamentary election due in 2014.

"We voted for the sake of our children. We want to get rid of the corrupt people and look forward to the future of our children and city," said 40-year-old Um Mohammed after casting her vote in Mosul.

The three provinces that make up the autonomous Kurdistan region in the north of Iraq hold elections on their own timetable and are scheduled to go to the polls in September.

Separately, the bodies of three men kidnapped on Wednesday were found handcuffed with bullets to the head and chest in the town of Sharqat, 260 km (160 miles) northwest of Baghdad. Two of the men were farmers and the third a policeman.

Sectarian tensions are running high in Iraq. The government has blamed attacks against both Sunni and Shi'ite Muslims on the al Qaeda-affiliated Islamic State of Iraq, which has been reinvigorated by the civil war in neighboring Syria.